Remark 2 
Kang, Kelly, Kühn, Osthus, and Pfenninger [1]} independently proved thm:pm. Furthermore they prove that when \(\ell = k-1\) , the \(\varepsilon \)  in the minimum degree, and thus also the \(\varepsilon \) -dependence in the threshold, can be removed thereby providing a tight result in this case and in particular providing a robust version of a result of Rödl, Ruciński, and Szemerédi [2]}.
